Update: the functionality used by the application was reverse engineered and Google stated that it may change. Google has released a statement which acknowledges that playing local content will come back to ChromeCast once the API has stabilised. Storm in a teacup, apparently.

Given that this is the second time they've purposefully removed/disabled[1] the ability to play media from external sources, it confirms some of my suspicions that I have had about the Chromecast developer program: the policy seems to be a heavy handed approach, where only approved content will be played through the device.